I would like to know how long it takes for a divorce if she leaves an we don't live together.

All perfect praise be to Allaah, The Lord of the Worlds. I testify that there is none worthy of worship except Allaah, and that Muhammad is His slave and Messenger. We ask Allaah to exalt his mention as well as that of his family and all his companions.

Basically, Islam encourages spouses to be patient and neglect the shortcomings of each other, because no body is perfect in this world. Islam calls its followers to be kind with each other and try their best (by fulfilling their duties) to have a happy and blissful marital life. However, if the disagreement reaches the point where all the doors of peaceful solution are blocked and no room is left to continue the married life then they may resort to divorce as a last solution. For details read Fatwa: 85044.

The marriage contract does not break if the wife leaves her house, or the husband and wife do not live together for a long period.

The divorce does not occur unless the husband divorces his wife or Muslim authorities declare divorce after looking into her case. See the Fatwa: 85034.

Allaah knows best.